Step |
Hyp |
Ref |
Expression |
1 |
|
suplesup.a |
|
2 |
|
suplesup.b |
|
3 |
|
suplesup.c |
|
4 |
|
ressxr |
|
5 |
1 4
|
sstrdi |
|
6 |
|
supxrcl |
|
7 |
5 6
|
syl |
|
8 |
7
|
adantr |
|
9 |
|
eqidd |
|
10 |
|
simpr |
|
11 |
|
peano2re |
|
12 |
11
|
adantl |
|
13 |
5
|
adantr |
|
14 |
|
supxrunb2 |
|
15 |
13 14
|
syl |
|
16 |
10 15
|
mpbird |
|
17 |
16
|
adantr |
|
18 |
|
breq1 |
|
19 |
18
|
rexbidv |
|
20 |
19
|
rspcva |
|
21 |
12 17 20
|
syl2anc |
|
22 |
|
1rp |
|
23 |
22
|
a1i |
|
24 |
3
|
r19.21bi |
|
25 |
|
oveq2 |
|
26 |
25
|
breq1d |
|
27 |
26
|
rexbidv |
|
28 |
27
|
rspcva |
|
29 |
23 24 28
|
syl2anc |
|
30 |
29
|
adantlr |
|
31 |
30
|
3adant3 |
|
32 |
|
nfv |
|
33 |
|
simp11r |
|
34 |
4 33
|
sseldi |
|
35 |
1
|
sselda |
|
36 |
|
1red |
|
37 |
35 36
|
resubcld |
|
38 |
37
|
adantlr |
|
39 |
38
|
3adant3 |
|
40 |
39
|
3ad2ant1 |
|
41 |
4 40
|
sseldi |
|
42 |
2
|
sselda |
|
43 |
42
|
adantlr |
|
44 |
43
|
3ad2antl1 |
|
45 |
44
|
3adant3 |
|
46 |
|
simp3 |
|
47 |
|
simp1r |
|
48 |
|
1red |
|
49 |
35
|
adantlr |
|
50 |
49
|
3adant3 |
|
51 |
47 48 50
|
ltaddsubd |
|
52 |
46 51
|
mpbid |
|
53 |
52
|
3ad2ant1 |
|
54 |
|
simp3 |
|
55 |
34 41 45 53 54
|
xrlttrd |
|
56 |
55
|
3exp |
|
57 |
32 56
|
reximdai |
|
58 |
31 57
|
mpd |
|
59 |
58
|
3exp |
|
60 |
59
|
adantlr |
|
61 |
60
|
rexlimdv |
|
62 |
21 61
|
mpd |
|
63 |
4
|
a1i |
|
64 |
63
|
sselda |
|
65 |
64
|
ad2antrr |
|
66 |
43
|
adantr |
|
67 |
|
simpr |
|
68 |
65 66 67
|
xrltled |
|
69 |
68
|
ex |
|
70 |
69
|
adantllr |
|
71 |
70
|
reximdva |
|
72 |
62 71
|
mpd |
|
73 |
72
|
ralrimiva |
|
74 |
|
supxrunb1 |
|
75 |
2 74
|
syl |
|
76 |
75
|
adantr |
|
77 |
73 76
|
mpbid |
|
78 |
9 10 77
|
3eqtr4d |
|
79 |
8 78
|
xreqled |
|
80 |
|
supeq1 |
|
81 |
|
xrsup0 |
|
82 |
81
|
a1i |
|
83 |
80 82
|
eqtrd |
|
84 |
83
|
adantl |
|
85 |
|
supxrcl |
|
86 |
2 85
|
syl |
|
87 |
|
mnfle |
|
88 |
86 87
|
syl |
|
89 |
88
|
adantr |
|
90 |
84 89
|
eqbrtrd |
|
91 |
90
|
adantlr |
|
92 |
|
simpll |
|
93 |
1
|
adantr |
|
94 |
|
neqne |
|
95 |
94
|
adantl |
|
96 |
|
supxrgtmnf |
|
97 |
93 95 96
|
syl2anc |
|
98 |
97
|
adantlr |
|
99 |
|
simpr |
|
100 |
|
simpl |
|
101 |
|
nltpnft |
|
102 |
100 7 101
|
3syl |
|
103 |
99 102
|
mtbid |
|
104 |
|
notnotr |
|
105 |
103 104
|
syl |
|
106 |
105
|
adantr |
|
107 |
98 106
|
jca |
|
108 |
92 7
|
syl |
|
109 |
|
xrrebnd |
|
110 |
108 109
|
syl |
|
111 |
107 110
|
mpbird |
|
112 |
|
nfv |
|
113 |
2
|
adantr |
|
114 |
|
simpr |
|
115 |
114
|
adantr |
|
116 |
|
simpr |
|
117 |
116
|
rphalfcld |
|
118 |
115 117
|
ltsubrpd |
|
119 |
5
|
ad2antrr |
|
120 |
|
rpre |
|
121 |
|
2re |
|
122 |
121
|
a1i |
|
123 |
|
2ne0 |
|
124 |
123
|
a1i |
|
125 |
120 122 124
|
redivcld |
|
126 |
125
|
adantl |
|
127 |
115 126
|
resubcld |
|
128 |
4 127
|
sseldi |
|
129 |
|
supxrlub |
|
130 |
119 128 129
|
syl2anc |
|
131 |
118 130
|
mpbid |
|
132 |
|
rphalfcl |
|
133 |
132
|
3ad2ant2 |
|
134 |
24
|
3adant2 |
|
135 |
|
oveq2 |
|
136 |
135
|
breq1d |
|
137 |
136
|
rexbidv |
|
138 |
137
|
rspcva |
|
139 |
133 134 138
|
syl2anc |
|
140 |
139
|
ad5ant134 |
|
141 |
|
recn |
|
142 |
141
|
adantr |
|
143 |
120
|
recnd |
|
144 |
143
|
adantl |
|
145 |
144
|
halfcld |
|
146 |
142 145 145
|
subsub4d |
|
147 |
143
|
2halvesd |
|
148 |
147
|
oveq2d |
|
149 |
148
|
adantl |
|
150 |
146 149
|
eqtr2d |
|
151 |
150
|
adantll |
|
152 |
151
|
adantr |
|
153 |
152
|
ad3antrrr |
|
154 |
127 126
|
resubcld |
|
155 |
154
|
adantr |
|
156 |
155
|
ad3antrrr |
|
157 |
4 156
|
sseldi |
|
158 |
120 49
|
sylanl2 |
|
159 |
125
|
ad2antlr |
|
160 |
158 159
|
resubcld |
|
161 |
160
|
adantllr |
|
162 |
161
|
ad3antrrr |
|
163 |
4 162
|
sseldi |
|
164 |
|
simp-6l |
|
165 |
|
simplr |
|
166 |
164 165 42
|
syl2anc |
|
167 |
|
simp-6r |
|
168 |
120
|
ad5antlr |
|
169 |
168
|
rehalfcld |
|
170 |
167 169
|
resubcld |
|
171 |
|
simp-4r |
|
172 |
164 171 35
|
syl2anc |
|
173 |
|
simpllr |
|
174 |
170 172 169 173
|
ltsub1dd |
|
175 |
|
simpr |
|
176 |
157 163 166 174 175
|
xrlttrd |
|
177 |
153 176
|
eqbrtrd |
|
178 |
177
|
ex |
|
179 |
178
|
reximdva |
|
180 |
140 179
|
mpd |
|
181 |
180
|
rexlimdva2 |
|
182 |
131 181
|
mpd |
|
183 |
112 113 114 182
|
supxrgere |
|
184 |
92 111 183
|
syl2anc |
|
185 |
91 184
|
pm2.61dan |
|
186 |
79 185
|
pm2.61dan |
|